Ratio word problem

[edc57]

My daughter is in Algebra 1 and she can earn 1 pt per week, if she attempts the problem of the week, and parental help is encouraged to involve the family.

The Current Problem of the Week --- Angela and Barry share some land. The ratio of the area of Angela’s portion to Barry’s is 3:2. Both grow corn and peas on their portion. The entire piece of land is planted in corn and peas in the ration 7:3. On Angela’s land, the ration of corn to peas is 4:1. Find the ratio of corn to peas on Barry’s land.

I noticed that this infamous word problem was posted in Dec. 2009. I read the help, but I need to know if our feeble attempt to follow your assistance is correct. Is the ration of corn to peas on Barry's land 1:4???

Your help was
Angela and Barry....
Angela has 3/5 of the land and 4/5 of that is planted with corn.
This 4/5 is (4/5)(3/5) of the total land, which is 12/25.
If corn covers 7/10 of the total land, then this is 35/50,
therefore Angela has corn on 24/50 of the entire land and Barry has (35-24)/50 of the entire land planted with corn.
As Barry has access to 20/50 of the entire land, then he has 20 parts in 50.
If 11 parts are corn, what is his ratio of corn to peas? Is the ration of corn to peas on Barry's land 1:4???

 

[JuicyBurger]

That's not the answer I got.

What I did was scale up the numbers, so the ratio of land is 30:20 (Angela:Barry).

This means that the total amount of land is 50.

Using these numbers, one can use the ratio of 7:3 corneas to figure out that a total of 35 units of land are used for corn, correct?

\(\displaystyle \frac{7}{10} * 50 = 35 \ \ units \ \ of \ \ land \ \ for \ \ corn\)

Now we know that Angela has 30 units of land out of the total of 50, and that the ratio of corn to peas is 4:1...

\(\displaystyle \frac{4}{5} * 30 = 24 \ \ units \ \ of \ \ land \ \ for \ \ corn\)

So now we know that Angela has a total of 24 out of 35 corn, so Barry must have the remaining 11 units of corn...

So barry has 11/20 units of corn, or a ratio of 11:9 for corn to peas.

Hope this helps!

 

[edc57]

Thank you so much! My husband & I were too embarrassed to contact my daughter's algebra tutor.

I read this hopeful quote on a posting here - In mathematics, you don't understand things. You just get used to them ......John von Neumann

 

[JuicyBurger]

Well, I have to say that John von Neumann definitely knows what he is talking about!